This typically means that they are less anxious if this an open field test, as mice are fearful of open spaces and prefer protected and/or darker environments. You could confirm by looking at levels of self grooming or rearing and fecal boli production, which are associated with anxiety. Additional confirmation tests, such as the light dark box test or an elevated platform would be useful as well. With a light dark box, you have light and dark chambers and record how long it takes the mouse to emerge into the lighted chamber and how much time it spends in each chamber. For the elevated platform test, record how long it takes for the mouse to crawl down from a moderately elevated platform in an empty cage. Sometimes it takes some trial and error to figure out the correct height for this, whethere or not you need bedding in the cage, etc.
I have always thought that there are likely to be stressor specific profiles for hormones, cytokines, and associated gene expression. Anxiety behaviors are typically expressed in response to some sort of stressor, so you could look at the methylome and/or transcriptome, and/or do endocrine or cytokine assays. I would look for data on endocrine responses to your behavioral tests, and use that as guide for molecular targets. Responses to stress often differ by strain and sex as well, so keep that mind.